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1 year ago

The price of apples went from $0.30 per lb to $0.90 per lb in three years. Find the rate of change of the price of apples.

Mathematics

2 answers:

Iteru [2.4K]1 year ago

8 0

<h2>Answer:</h2>

Hence, the rate of change of the price of apples is:

$ 0.20 per year.

<h2>Step-by-step explanation:</h2>

Let P denote the price of apples.

It is given that the initial price of apples is: $ 0.30 per lb.

i.e. P(0)=$ 0.30 per lb.

Also, the price of the apples after three years is: $ 0.90 per lb.

i.e. P(3)=$ 0.90 per lb.

Hence, the rate of the change of the price of apples is calculated by:

$Rate\ of\ change=\dfrac{P(3)-P(0)}{3-0}$

Now on putting the value in the formula we obtain:

$Rate\ of\ change=\dfrac{0.90-0.30}{3-0}\\\\\\Rate\ of\ change=\dfrac{0.60}{3}\\\\\\Rate\ of\ change=0.20$

The rate of change is:

$ 0.20 per year.

Brut [27]1 year ago

3 0

90c-30c=60cent change

60cents/3years=20cents/year

It changed 20cents a year

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Zolol [24]

Answer:

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Step-by-step explanation:

Given area of circular pond = 78.5 square yd

To find the diameter of the pond.

Solution:

The pond being circular in shape, the area of pond can be given as:

⇒ $\pi\ r^2$

where $r$ represents radius of the pond.

Thus, we have:

⇒ $\pi\ r^2=78.5$

Using $\pi=3.14$

⇒ $3.14r^2=78.5$

Solving for $r$

Dividing both sides by 3.14

⇒ $\frac{3.14r^2}{3.14}=\frac{78.5}{3.14}$

⇒ $r^2=25$

Taking square root both sides.

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Thus, diameter of pound = 10 yd

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1 year ago

We flip a fair coin five times. For every heads you pay me $1 and for every tails I pay you $1. Let X denote the my net winning

TEA [102]

Answer:

The probability mass of X is 0.03

Step-by-step explanation:

If we set the winning requirement of your heads and my tails then the occurring possibility of both is 1/2 or 0.5.

Hence let us make a graph and use the figures to calculate the all the probabilities of you getting a heads.

Where X represents the number of dollars won during the flip of the coin, probability of heads represent the chances of occurrence of the value and of winning the dollars.

The probability of winning start to drop as the winning amount increases.

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1 year ago

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x? StartFraction 2 Over 11 EndFraction plus-or-minus

slamgirl [31]

Answer:

$x=\frac{2}{11}\pm\frac{\sqrt{15}} {11}$

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$11x^{2} -4x=1$

equate to zero

$11x^{2} -4x-1=0$

$a=11\\b=-4\\c=-1$

substitute in the formula

$x=\frac{-(-4)\pm\sqrt{-4^{2}-4(11)(-1)}} {2(11)}$

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$x=\frac{2\pm\sqrt{15}} {11}$

$x=\frac{2}{11}\pm\frac{\sqrt{15}} {11}$

therefore

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1 year ago

Read 2 more answers

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dolphi86 [110]

4 days 10 days Cross Multiplication
---------- = ------------
7 mins x

4x = 7*10
4x = 70
x = 70/4
x = 17.5

17.5 minutes = x

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1 year ago

How many solutions does the equation sin(5x) = 1/2 have on the interval (0, 2PI]

Darina [25.2K]

Answer:

Step-by-step explanation:

Given the equation

Sin(5x) = ½

5x = arcSin(½)

5x = 30°

Then,

The general formula for sin is

5θ = n180 + (-1)ⁿθ

Divide through by 5

θ = n•36 + (-1)ⁿ30/5

θ = 36n + (-1)ⁿ6

The range of the solution is

0<θ<2π I.e 0<θ<360

First solution

When n = 0

θ = 36n + (-1)ⁿθ

θ = 0×36 + (-1)^0×6

θ = 6°

When n = 1

θ = 36n + (-1)ⁿ6

θ = 36-6

θ = 30°

When n = 2

θ = 36n + (-1)ⁿ6

θ = 36×2 + 6

θ = 78°

When n =3

θ = 36n + (-1)ⁿ6

θ = 36×3 - 6

θ = 102°

When n=4

θ = 36n + (-1)ⁿ6

θ = 36×4 + 6

θ = 150

When n =5

θ = 36n + (-1)ⁿ6

θ = 36×5 - 6

θ = 174°

When n = 6

θ = 36n+ (-1)ⁿ6

θ = 36×6 + 6

θ = 222°

When n = 7

θ = 36n + (-1)ⁿ6

θ = 36×7 - 6

θ = 246°

When n =8

θ = 36n + (-1)ⁿ6

θ = 36×8 + 6

θ = 294°

When n =9

θ = 36n + (-1)ⁿ6

θ = 36×9 - 6

θ = 318°

When n =10

θ = 36n + (-1)ⁿ6

θ = 36×10 + 6

θ = 366°

When n = 10 is out of range of θ

Then, the solution is from n =0 to n=9

So the equation have 10 solutions in the range 0<θ<2π

4 0

1 year ago